Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 136.2 | ||
Root | \(0.0437845 - 0.134755i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.136 |
Dual form | 225.2.h.d.91.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.114629 | + | 0.0832830i | −0.0810551 | + | 0.0588900i | −0.627575 | − | 0.778556i | \(-0.715952\pi\) |
0.546520 | + | 0.837446i | \(0.315952\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.611830 | + | 1.88302i | −0.305915 | + | 0.941510i | ||||
\(5\) | −2.14898 | + | 0.617963i | −0.961054 | + | 0.276362i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.858311 | −0.324411 | −0.162205 | − | 0.986757i | \(-0.551861\pi\) | ||||
−0.162205 | + | 0.986757i | \(0.551861\pi\) | |||||||
\(8\) | −0.174259 | − | 0.536314i | −0.0616098 | − | 0.189615i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.194870 | − | 0.249810i | 0.0616234 | − | 0.0789969i | ||||
\(11\) | −2.97713 | + | 2.16301i | −0.897637 | + | 0.652171i | −0.937858 | − | 0.347019i | \(-0.887194\pi\) |
0.0402210 | + | 0.999191i | \(0.487194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.70638 | − | 2.69285i | −1.02797 | − | 0.746861i | −0.0600653 | − | 0.998194i | \(-0.519131\pi\) |
−0.967901 | + | 0.251334i | \(0.919131\pi\) | |||||||
\(14\) | 0.0983875 | − | 0.0714827i | 0.0262952 | − | 0.0191045i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.13894 | − | 2.28058i | −0.784736 | − | 0.570144i | ||||
\(17\) | 1.63996 | + | 5.04728i | 0.397749 | + | 1.22414i | 0.926800 | + | 0.375555i | \(0.122548\pi\) |
−0.529052 | + | 0.848590i | \(0.677452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.96804 | + | 6.05699i | 0.451499 | + | 1.38957i | 0.875197 | + | 0.483766i | \(0.160732\pi\) |
−0.423699 | + | 0.905803i | \(0.639268\pi\) | |||||||
\(20\) | 0.151175 | − | 4.42466i | 0.0338037 | − | 0.989385i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.161124 | − | 0.495888i | 0.0343517 | − | 0.105724i | ||||
\(23\) | 2.76990 | − | 2.01245i | 0.577564 | − | 0.419625i | −0.260281 | − | 0.965533i | \(-0.583815\pi\) |
0.837845 | + | 0.545908i | \(0.183815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.23624 | − | 2.65598i | 0.847249 | − | 0.531197i | ||||
\(26\) | 0.649128 | 0.127304 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.525140 | − | 1.61622i | 0.0992422 | − | 0.305436i | ||||
\(29\) | −1.15388 | + | 3.55129i | −0.214271 | + | 0.659458i | 0.784934 | + | 0.619580i | \(0.212697\pi\) |
−0.999205 | + | 0.0398784i | \(0.987303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.387167 | + | 1.19158i | 0.0695373 | + | 0.214014i | 0.979786 | − | 0.200048i | \(-0.0641098\pi\) |
−0.910249 | + | 0.414062i | \(0.864110\pi\) | |||||||
\(32\) | 1.67757 | 0.296556 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.608340 | − | 0.441985i | −0.104329 | − | 0.0757997i | ||||
\(35\) | 1.84449 | − | 0.530404i | 0.311776 | − | 0.0896547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.02772 | + | 4.37939i | 0.990951 | + | 0.719968i | 0.960129 | − | 0.279557i | \(-0.0901876\pi\) |
0.0308218 | + | 0.999525i | \(0.490188\pi\) | |||||||
\(38\) | −0.730039 | − | 0.530404i | −0.118428 | − | 0.0860430i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.705901 | + | 1.04484i | 0.111613 | + | 0.165204i | ||||
\(41\) | −2.04817 | − | 1.48808i | −0.319870 | − | 0.232399i | 0.416250 | − | 0.909250i | \(-0.363344\pi\) |
−0.736120 | + | 0.676851i | \(0.763344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.37972 | −0.515402 | −0.257701 | − | 0.966225i | \(-0.582965\pi\) | ||||
−0.257701 | + | 0.966225i | \(0.582965\pi\) | |||||||
\(44\) | −2.25149 | − | 6.92938i | −0.339425 | − | 1.04464i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.149909 | + | 0.461371i | −0.0221028 | + | 0.0680255i | ||||
\(47\) | 2.62645 | − | 8.08338i | 0.383107 | − | 1.17908i | −0.554737 | − | 0.832026i | \(-0.687181\pi\) |
0.937844 | − | 0.347057i | \(-0.112819\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.26330 | −0.894758 | ||||||||
\(50\) | −0.264399 | + | 0.657260i | −0.0373917 | + | 0.0929506i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.33836 | − | 5.33163i | 1.01765 | − | 0.739364i | ||||
\(53\) | 0.725656 | − | 2.23334i | 0.0996765 | − | 0.306773i | −0.888768 | − | 0.458358i | \(-0.848438\pi\) |
0.988444 | + | 0.151585i | \(0.0484378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.06113 | − | 6.48802i | 0.682442 | − | 0.874844i | ||||
\(56\) | 0.149568 | + | 0.460324i | 0.0199869 | + | 0.0615133i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.163493 | − | 0.503181i | −0.0214677 | − | 0.0660709i | ||||
\(59\) | 10.6195 | + | 7.71550i | 1.38254 | + | 1.00447i | 0.996638 | + | 0.0819317i | \(0.0261089\pi\) |
0.385900 | + | 0.922541i | \(0.373891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.37141 | + | 6.08218i | −1.07185 | + | 0.778744i | −0.976244 | − | 0.216676i | \(-0.930479\pi\) |
−0.0956052 | + | 0.995419i | \(0.530479\pi\) | |||||||
\(62\) | −0.143619 | − | 0.104345i | −0.0182396 | − | 0.0132519i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.08559 | − | 4.42144i | 0.760698 | − | 0.552680i | ||||
\(65\) | 9.62903 | + | 3.49647i | 1.19433 | + | 0.433683i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.03412 | + | 3.18270i | 0.126338 | + | 0.388828i | 0.994142 | − | 0.108077i | \(-0.0344695\pi\) |
−0.867805 | + | 0.496906i | \(0.834469\pi\) | |||||||
\(68\) | −10.5075 | −1.27422 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.167259 | + | 0.214415i | −0.0199913 | + | 0.0256275i | ||||
\(71\) | 1.33585 | − | 4.11131i | 0.158536 | − | 0.487923i | −0.839966 | − | 0.542639i | \(-0.817425\pi\) |
0.998502 | + | 0.0547158i | \(0.0174253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34593 | − | 5.33713i | 0.859776 | − | 0.624664i | −0.0680477 | − | 0.997682i | \(-0.521677\pi\) |
0.927824 | + | 0.373018i | \(0.121677\pi\) | |||||||
\(74\) | −1.05568 | −0.122721 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.6095 | −1.44641 | ||||||||
\(77\) | 2.55530 | − | 1.85653i | 0.291203 | − | 0.211572i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00347 | + | 3.08837i | −0.112899 | + | 0.347469i | −0.991503 | − | 0.130083i | \(-0.958476\pi\) |
0.878604 | + | 0.477552i | \(0.158476\pi\) | |||||||
\(80\) | 8.15484 | + | 2.96116i | 0.911739 | + | 0.331068i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.358712 | 0.0396131 | ||||||||
\(83\) | 2.28447 | + | 7.03087i | 0.250753 | + | 0.771738i | 0.994637 | + | 0.103429i | \(0.0329815\pi\) |
−0.743884 | + | 0.668309i | \(0.767019\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.64327 | − | 9.83307i | −0.720564 | − | 1.06655i | ||||
\(86\) | 0.387414 | − | 0.281473i | 0.0417760 | − | 0.0303520i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.67884 | + | 1.21975i | 0.178965 | + | 0.130026i | ||||
\(89\) | −12.5378 | + | 9.10921i | −1.32900 | + | 0.965575i | −0.329227 | + | 0.944251i | \(0.606788\pi\) |
−0.999773 | + | 0.0213236i | \(0.993212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.18123 | + | 2.31130i | 0.333483 | + | 0.242290i | ||||
\(92\) | 2.09478 | + | 6.44705i | 0.218395 | + | 0.672152i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.372140 | + | 1.14533i | 0.0383833 | + | 0.118132i | ||||
\(95\) | −7.97227 | − | 11.8002i | −0.817938 | − | 1.21067i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.10209 | + | 9.54725i | −0.314970 | + | 0.969377i | 0.660797 | + | 0.750564i | \(0.270218\pi\) |
−0.975767 | + | 0.218812i | \(0.929782\pi\) | |||||||
\(98\) | 0.717957 | − | 0.521627i | 0.0725247 | − | 0.0526922i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.40941 | + | 9.60194i | 0.240941 | + | 0.960194i | ||||
\(101\) | 0.714616 | 0.0711070 | 0.0355535 | − | 0.999368i | \(-0.488681\pi\) | ||||
0.0355535 | + | 0.999368i | \(0.488681\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.241269 | − | 0.742551i | 0.0237730 | − | 0.0731657i | −0.938466 | − | 0.345371i | \(-0.887753\pi\) |
0.962239 | + | 0.272205i | \(0.0877530\pi\) | |||||||
\(104\) | −0.798339 | + | 2.45704i | −0.0782836 | + | 0.240932i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.102818 | + | 0.316441i | 0.00998655 | + | 0.0307354i | ||||
\(107\) | −11.9601 | −1.15623 | −0.578113 | − | 0.815957i | \(-0.696211\pi\) | ||||
−0.578113 | + | 0.815957i | \(0.696211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.96902 | − | 1.43057i | −0.188598 | − | 0.137024i | 0.489480 | − | 0.872015i | \(-0.337187\pi\) |
−0.678078 | + | 0.734990i | \(0.737187\pi\) | |||||||
\(110\) | −0.0398114 | + | 1.16522i | −0.00379587 | + | 0.111100i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.69419 | + | 1.95744i | 0.254577 | + | 0.184961i | ||||
\(113\) | −12.9729 | − | 9.42535i | −1.22039 | − | 0.886662i | −0.224254 | − | 0.974531i | \(-0.571994\pi\) |
−0.996132 | + | 0.0878685i | \(0.971994\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.70884 | + | 6.03642i | −0.439102 | + | 0.562899i | ||||
\(116\) | −5.98117 | − | 4.34558i | −0.555338 | − | 0.403477i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.85987 | −0.171215 | ||||||||
\(119\) | −1.40759 | − | 4.33213i | −0.129034 | − | 0.397126i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.785483 | − | 2.41747i | 0.0714076 | − | 0.219770i | ||||
\(122\) | 0.453065 | − | 1.39439i | 0.0410186 | − | 0.126242i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.48065 | −0.222769 | ||||||||
\(125\) | −7.46231 | + | 8.32550i | −0.667449 | + | 0.744655i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.10539 | − | 2.25620i | 0.275559 | − | 0.200205i | −0.441419 | − | 0.897301i | \(-0.645525\pi\) |
0.716978 | + | 0.697096i | \(0.245525\pi\) | |||||||
\(128\) | −1.36615 | + | 4.20459i | −0.120752 | + | 0.371637i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.39496 | + | 0.401137i | −0.122346 | + | 0.0351821i | ||||
\(131\) | 3.84709 | + | 11.8401i | 0.336122 | + | 1.03448i | 0.966167 | + | 0.257919i | \(0.0830367\pi\) |
−0.630044 | + | 0.776559i | \(0.716963\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.68919 | − | 5.19878i | −0.146471 | − | 0.450791i | ||||
\(134\) | −0.383605 | − | 0.278705i | −0.0331384 | − | 0.0240765i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.42115 | − | 1.75907i | 0.207611 | − | 0.150839i | ||||
\(137\) | −9.59406 | − | 6.97049i | −0.819676 | − | 0.595529i | 0.0969439 | − | 0.995290i | \(-0.469093\pi\) |
−0.916620 | + | 0.399761i | \(0.869093\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.77074 | − | 2.73960i | 0.319830 | − | 0.232370i | −0.416273 | − | 0.909240i | \(-0.636664\pi\) |
0.736103 | + | 0.676870i | \(0.236664\pi\) | |||||||
\(140\) | −0.129755 | + | 3.79773i | −0.0109663 | + | 0.320967i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.189275 | + | 0.582530i | 0.0158836 | + | 0.0488848i | ||||
\(143\) | 16.8590 | 1.40982 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.285109 | − | 8.34472i | 0.0236770 | − | 0.692991i | ||||
\(146\) | −0.397566 | + | 1.22358i | −0.0329028 | + | 0.101264i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.9344 | + | 8.67087i | −0.981004 | + | 0.712741i | ||||
\(149\) | 11.5480 | 0.946053 | 0.473026 | − | 0.881048i | \(-0.343162\pi\) | ||||
0.473026 | + | 0.881048i | \(0.343162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.4694 | 1.99129 | 0.995646 | − | 0.0932103i | \(-0.0297129\pi\) | ||||
0.995646 | + | 0.0932103i | \(0.0297129\pi\) | |||||||
\(152\) | 2.90550 | − | 2.11097i | 0.235667 | − | 0.171222i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.138294 | + | 0.425626i | −0.0111441 | + | 0.0342979i | ||||
\(155\) | −1.56837 | − | 2.32143i | −0.125974 | − | 0.186461i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.3660 | −1.78500 | −0.892501 | − | 0.451045i | \(-0.851052\pi\) | ||||
−0.892501 | + | 0.451045i | \(0.851052\pi\) | |||||||
\(158\) | −0.142181 | − | 0.437589i | −0.0113113 | − | 0.0348127i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.60508 | + | 1.03668i | −0.285006 | + | 0.0819567i | ||||
\(161\) | −2.37743 | + | 1.72731i | −0.187368 | + | 0.136131i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.658095 | + | 0.478134i | 0.0515460 | + | 0.0374503i | 0.613260 | − | 0.789881i | \(-0.289858\pi\) |
−0.561714 | + | 0.827332i | \(0.689858\pi\) | |||||||
\(164\) | 4.05522 | − | 2.94629i | 0.316659 | − | 0.230067i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.847418 | − | 0.615685i | −0.0657724 | − | 0.0477865i | ||||
\(167\) | 7.77671 | + | 23.9343i | 0.601780 | + | 1.85209i | 0.517572 | + | 0.855640i | \(0.326836\pi\) |
0.0842082 | + | 0.996448i | \(0.473164\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.46864 | + | 7.59770i | 0.189896 | + | 0.584438i | ||||
\(170\) | 1.58044 | + | 0.573885i | 0.121214 | + | 0.0440150i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.06781 | − | 6.36408i | 0.157669 | − | 0.485256i | ||||
\(173\) | 0.332462 | − | 0.241548i | 0.0252766 | − | 0.0183645i | −0.575075 | − | 0.818101i | \(-0.695027\pi\) |
0.600352 | + | 0.799736i | \(0.295027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.63601 | + | 2.27966i | −0.274857 | + | 0.172326i | ||||
\(176\) | 14.2779 | 1.07624 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.678550 | − | 2.08836i | 0.0508595 | − | 0.156529i | ||||
\(179\) | 4.58896 | − | 14.1234i | 0.342995 | − | 1.05563i | −0.619653 | − | 0.784876i | \(-0.712727\pi\) |
0.962648 | − | 0.270755i | \(-0.0872733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.228432 | + | 0.703043i | 0.0169792 | + | 0.0522568i | 0.959187 | − | 0.282772i | \(-0.0912540\pi\) |
−0.942208 | + | 0.335029i | \(0.891254\pi\) | |||||||
\(182\) | −0.557153 | −0.0412990 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.56198 | − | 1.13485i | −0.115151 | − | 0.0836621i | ||||
\(185\) | −15.6598 | − | 5.68633i | −1.15133 | − | 0.418067i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.7997 | − | 11.4791i | −1.15539 | − | 0.839437i | ||||
\(188\) | 13.6142 | + | 9.89131i | 0.992920 | + | 0.721398i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.89661 | + | 0.688692i | 0.137595 | + | 0.0499630i | ||||
\(191\) | −2.20462 | − | 1.60175i | −0.159521 | − | 0.115899i | 0.505161 | − | 0.863025i | \(-0.331433\pi\) |
−0.664682 | + | 0.747126i | \(0.731433\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.2040 | 1.02243 | 0.511215 | − | 0.859453i | \(-0.329196\pi\) | ||||
0.511215 | + | 0.859453i | \(0.329196\pi\) | |||||||
\(194\) | −0.439534 | − | 1.35275i | −0.0315567 | − | 0.0971215i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.83208 | − | 11.7939i | 0.273720 | − | 0.842423i | ||||
\(197\) | 1.71378 | − | 5.27447i | 0.122102 | − | 0.375791i | −0.871260 | − | 0.490821i | \(-0.836697\pi\) |
0.993362 | + | 0.115031i | \(0.0366967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.96371 | 0.422756 | 0.211378 | − | 0.977404i | \(-0.432205\pi\) | ||||
0.211378 | + | 0.977404i | \(0.432205\pi\) | |||||||
\(200\) | −2.16264 | − | 1.80913i | −0.152922 | − | 0.127925i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.0819159 | + | 0.0595154i | −0.00576358 | + | 0.00418749i | ||||
\(203\) | 0.990391 | − | 3.04811i | 0.0695119 | − | 0.213935i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.32106 | + | 1.93217i | 0.371639 | + | 0.134948i | ||||
\(206\) | 0.0341853 | + | 0.105212i | 0.00238181 | + | 0.00733044i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.49289 | + | 16.9054i | 0.380863 | + | 1.17218i | ||||
\(209\) | −18.9604 | − | 13.7755i | −1.31152 | − | 0.952875i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0983 | − | 8.06342i | 0.764042 | − | 0.555109i | −0.136106 | − | 0.990694i | \(-0.543459\pi\) |
0.900147 | + | 0.435586i | \(0.143459\pi\) | |||||||
\(212\) | 3.76144 | + | 2.73285i | 0.258337 | + | 0.187693i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.37098 | − | 0.996073i | 0.0937180 | − | 0.0680901i | ||||
\(215\) | 7.26295 | − | 2.08854i | 0.495329 | − | 0.142437i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.332310 | − | 1.02274i | −0.0225587 | − | 0.0694284i | ||||
\(218\) | 0.344849 | 0.0233561 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.12052 | + | 13.4998i | 0.614905 | + | 0.910154i | ||||
\(221\) | 7.51322 | − | 23.1233i | 0.505394 | − | 1.55544i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.62259 | + | 1.90543i | −0.175622 | + | 0.127597i | −0.672124 | − | 0.740439i | \(-0.734618\pi\) |
0.496502 | + | 0.868036i | \(0.334618\pi\) | |||||||
\(224\) | −1.43988 | −0.0962060 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.27204 | 0.151134 | ||||||||
\(227\) | 10.6627 | − | 7.74694i | 0.707711 | − | 0.514182i | −0.174723 | − | 0.984618i | \(-0.555903\pi\) |
0.882434 | + | 0.470435i | \(0.155903\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.80407 | − | 5.55236i | 0.119216 | − | 0.366911i | −0.873587 | − | 0.486669i | \(-0.838212\pi\) |
0.992803 | + | 0.119758i | \(0.0382119\pi\) | |||||||
\(230\) | 0.0370403 | − | 1.08412i | 0.00244237 | − | 0.0714845i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.10568 | 0.138245 | ||||||||
\(233\) | −2.88453 | − | 8.87767i | −0.188972 | − | 0.581595i | 0.811022 | − | 0.585015i | \(-0.198911\pi\) |
−0.999994 | + | 0.00341975i | \(0.998911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.648959 | + | 18.9941i | −0.0423334 | + | 1.23904i | ||||
\(236\) | −21.0258 | + | 15.2761i | −1.36866 | + | 0.994390i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.522144 | + | 0.379360i | 0.0338456 | + | 0.0245903i | ||||
\(239\) | 13.8748 | − | 10.0806i | 0.897485 | − | 0.652061i | −0.0403340 | − | 0.999186i | \(-0.512842\pi\) |
0.937819 | + | 0.347125i | \(0.112842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.84169 | − | 4.24424i | −0.376296 | − | 0.273395i | 0.383521 | − | 0.923532i | \(-0.374711\pi\) |
−0.759817 | + | 0.650137i | \(0.774711\pi\) | |||||||
\(242\) | 0.111295 | + | 0.342530i | 0.00715430 | + | 0.0220187i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.33099 | − | 19.4848i | −0.405300 | − | 1.24739i | ||||
\(245\) | 13.4597 | − | 3.87049i | 0.859910 | − | 0.247277i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.01625 | − | 27.7492i | 0.573690 | − | 1.76564i | ||||
\(248\) | 0.571593 | − | 0.415286i | 0.0362962 | − | 0.0263707i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.162026 | − | 1.57583i | 0.0102474 | − | 0.0996642i | ||||
\(251\) | 5.75708 | 0.363383 | 0.181692 | − | 0.983356i | \(-0.441843\pi\) | ||||
0.181692 | + | 0.983356i | \(0.441843\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.89339 | + | 11.9826i | −0.244776 | + | 0.753342i | ||||
\(254\) | −0.168066 | + | 0.517253i | −0.0105454 | + | 0.0324553i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.45541 | + | 13.7123i | 0.278463 | + | 0.857021i | ||||
\(257\) | −26.9602 | −1.68173 | −0.840867 | − | 0.541242i | \(-0.817954\pi\) | ||||
−0.840867 | + | 0.541242i | \(0.817954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.17365 | − | 3.75888i | −0.321475 | − | 0.233565i | ||||
\(260\) | −12.4752 | + | 15.9924i | −0.773682 | + | 0.991807i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.42707 | − | 1.03683i | −0.0881648 | − | 0.0640555i | ||||
\(263\) | 16.7202 | + | 12.1479i | 1.03101 | + | 0.749073i | 0.968511 | − | 0.248972i | \(-0.0800926\pi\) |
0.0625002 | + | 0.998045i | \(0.480093\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.179299 | + | 5.24783i | −0.0110143 | + | 0.322372i | ||||
\(266\) | 0.626600 | + | 0.455252i | 0.0384193 | + | 0.0279133i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.62579 | −0.404734 | ||||||||
\(269\) | 4.24699 | + | 13.0709i | 0.258943 | + | 0.796946i | 0.993027 | + | 0.117887i | \(0.0376120\pi\) |
−0.734084 | + | 0.679059i | \(0.762388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.03333 | − | 3.18025i | 0.0627701 | − | 0.193187i | −0.914754 | − | 0.404012i | \(-0.867615\pi\) |
0.977524 | + | 0.210826i | \(0.0676153\pi\) | |||||||
\(272\) | 6.36296 | − | 19.5832i | 0.385811 | − | 1.18740i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.68028 | 0.101510 | ||||||||
\(275\) | −6.86691 | + | 17.0702i | −0.414090 | + | 1.02937i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.20791 | + | 5.23685i | −0.433081 | + | 0.314652i | −0.782880 | − | 0.622173i | \(-0.786250\pi\) |
0.349799 | + | 0.936825i | \(0.386250\pi\) | |||||||
\(278\) | −0.204075 | + | 0.628077i | −0.0122396 | + | 0.0376696i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.605882 | − | 0.896799i | −0.0362084 | − | 0.0535940i | ||||
\(281\) | 6.95019 | + | 21.3905i | 0.414613 | + | 1.27605i | 0.912596 | + | 0.408862i | \(0.134074\pi\) |
−0.497983 | + | 0.867187i | \(0.665926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.403866 | + | 1.24297i | 0.0240073 | + | 0.0738870i | 0.962342 | − | 0.271840i | \(-0.0876322\pi\) |
−0.938335 | + | 0.345727i | \(0.887632\pi\) | |||||||
\(284\) | 6.92437 | + | 5.03085i | 0.410886 | + | 0.298526i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.93254 | + | 1.40407i | −0.114273 | + | 0.0830243i | ||||
\(287\) | 1.75797 | + | 1.27724i | 0.103769 | + | 0.0753929i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.03225 | + | 6.56231i | −0.531309 | + | 0.386018i | ||||
\(290\) | 0.662291 | + | 0.980293i | 0.0388911 | + | 0.0575648i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.55546 | + | 17.0980i | 0.325109 | + | 1.00058i | ||||
\(293\) | −1.97058 | −0.115123 | −0.0575613 | − | 0.998342i | \(-0.518332\pi\) | ||||
−0.0575613 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.5889 | − | 10.0180i | −1.60629 | − | 0.583272i | ||||
\(296\) | 1.29835 | − | 3.99590i | 0.0754648 | − | 0.232257i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.32374 | + | 0.961756i | −0.0766824 | + | 0.0557130i | ||||
\(299\) | −15.6855 | −0.907118 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.90085 | 0.167202 | ||||||||
\(302\) | −2.80491 | + | 2.03789i | −0.161404 | + | 0.117267i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.63588 | − | 23.5008i | 0.437948 | − | 1.34786i | ||||
\(305\) | 14.2314 | − | 18.2437i | 0.814889 | − | 1.04463i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2544 | −0.870617 | −0.435308 | − | 0.900281i | \(-0.643361\pi\) | ||||
−0.435308 | + | 0.900281i | \(0.643361\pi\) | |||||||
\(308\) | 1.93248 | + | 5.94756i | 0.110113 | + | 0.338894i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.373116 | + | 0.135485i | 0.0211916 | + | 0.00769502i | ||||
\(311\) | 14.3562 | − | 10.4304i | 0.814065 | − | 0.591453i | −0.100941 | − | 0.994892i | \(-0.532185\pi\) |
0.915006 | + | 0.403439i | \(0.132185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.1565 | + | 16.0976i | 1.25236 | + | 0.909890i | 0.998356 | − | 0.0573136i | \(-0.0182535\pi\) |
0.254001 | + | 0.967204i | \(0.418253\pi\) | |||||||
\(314\) | 2.56380 | − | 1.86271i | 0.144684 | − | 0.105119i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.20150 | − | 3.77911i | −0.292607 | − | 0.212592i | ||||
\(317\) | −2.67165 | − | 8.22248i | −0.150055 | − | 0.461821i | 0.847572 | − | 0.530681i | \(-0.178064\pi\) |
−0.997626 | + | 0.0688603i | \(0.978064\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.24621 | − | 13.0685i | −0.237742 | − | 0.731696i | ||||
\(320\) | −10.3455 | + | 13.2623i | −0.578333 | + | 0.741383i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.128668 | − | 0.396000i | 0.00717039 | − | 0.0220682i | ||||
\(323\) | −27.3438 | + | 19.8664i | −1.52145 | + | 1.10540i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.8533 | − | 1.56345i | −1.26767 | − | 0.0867248i | ||||
\(326\) | −0.115257 | −0.00638351 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.441167 | + | 1.35777i | −0.0243594 | + | 0.0749704i | ||||
\(329\) | −2.25431 | + | 6.93805i | −0.124284 | + | 0.382507i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.53353 | + | 4.71971i | 0.0842903 | + | 0.259419i | 0.984315 | − | 0.176420i | \(-0.0564517\pi\) |
−0.900025 | + | 0.435839i | \(0.856452\pi\) | |||||||
\(332\) | −14.6370 | −0.803308 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.88475 | − | 2.09590i | −0.157847 | − | 0.114682i | ||||
\(335\) | −4.18910 | − | 6.20051i | −0.228875 | − | 0.338770i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.91011 | + | 4.29394i | 0.321944 | + | 0.233906i | 0.737005 | − | 0.675888i | \(-0.236240\pi\) |
−0.415061 | + | 0.909794i | \(0.636240\pi\) | |||||||
\(338\) | −0.915738 | − | 0.665322i | −0.0498096 | − | 0.0361888i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 22.5804 | − | 6.49325i | 1.22460 | − | 0.352146i | ||||
\(341\) | −3.73004 | − | 2.71003i | −0.201993 | − | 0.146757i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.3840 | 0.614680 | ||||||||
\(344\) | 0.588946 | + | 1.81259i | 0.0317538 | + | 0.0977282i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0179930 | + | 0.0553768i | −0.000967311 | + | 0.00297708i | ||||
\(347\) | −4.92493 | + | 15.1574i | −0.264384 | + | 0.813691i | 0.727450 | + | 0.686160i | \(0.240705\pi\) |
−0.991835 | + | 0.127531i | \(0.959295\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5844 | 0.887743 | 0.443871 | − | 0.896091i | \(-0.353605\pi\) | ||||
0.443871 | + | 0.896091i | \(0.353605\pi\) | |||||||
\(350\) | 0.226936 | − | 0.564133i | 0.0121303 | − | 0.0301542i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.99435 | + | 3.62861i | −0.266200 | + | 0.193405i | ||||
\(353\) | −4.00768 | + | 12.3344i | −0.213307 | + | 0.656492i | 0.785962 | + | 0.618275i | \(0.212168\pi\) |
−0.999269 | + | 0.0382177i | \(0.987832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.330069 | + | 9.66063i | −0.0175182 | + | 0.512733i | ||||
\(356\) | −9.48185 | − | 29.1821i | −0.502537 | − | 1.54665i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.650208 | + | 2.00113i | 0.0343646 | + | 0.105763i | ||||
\(359\) | −10.9153 | − | 7.93042i | −0.576087 | − | 0.418551i | 0.261225 | − | 0.965278i | \(-0.415874\pi\) |
−0.837311 | + | 0.546727i | \(0.815874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4427 | + | 12.6728i | −0.918036 | + | 0.666992i | ||||
\(362\) | −0.0847365 | − | 0.0615647i | −0.00445365 | − | 0.00323577i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.29859 | + | 4.57619i | −0.330136 | + | 0.239858i | ||||
\(365\) | −12.4881 | + | 16.0089i | −0.653658 | + | 0.837945i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.41364 | + | 4.35073i | 0.0737913 | + | 0.227106i | 0.981149 | − | 0.193253i | \(-0.0619039\pi\) |
−0.907358 | + | 0.420360i | \(0.861904\pi\) | |||||||
\(368\) | −13.2841 | −0.692482 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.26864 | − | 0.652373i | 0.117941 | − | 0.0339152i | ||||
\(371\) | −0.622838 | + | 1.91690i | −0.0323361 | + | 0.0995204i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.7841 | − | 12.1944i | 0.869048 | − | 0.631401i | −0.0612830 | − | 0.998120i | \(-0.519519\pi\) |
0.930331 | + | 0.366720i | \(0.119519\pi\) | |||||||
\(374\) | 2.76712 | 0.143084 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.79291 | −0.247175 | ||||||||
\(377\) | 13.8398 | − | 10.0552i | 0.712787 | − | 0.517870i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.78662 | + | 5.49865i | −0.0917725 | + | 0.282447i | −0.986399 | − | 0.164368i | \(-0.947442\pi\) |
0.894627 | + | 0.446815i | \(0.147442\pi\) | |||||||
\(380\) | 27.0977 | − | 7.79223i | 1.39008 | − | 0.399733i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.386113 | 0.0197553 | ||||||||
\(383\) | −7.97647 | − | 24.5491i | −0.407579 | − | 1.25440i | −0.918723 | − | 0.394903i | \(-0.870778\pi\) |
0.511144 | − | 0.859495i | \(-0.329222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.34402 | + | 5.56873i | −0.221392 | + | 0.283809i | ||||
\(386\) | −1.62820 | + | 1.18295i | −0.0828731 | + | 0.0602108i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.0797 | − | 11.6826i | −0.816324 | − | 0.593094i | ||||
\(389\) | −12.7053 | + | 9.23092i | −0.644183 | + | 0.468026i | −0.861285 | − | 0.508123i | \(-0.830340\pi\) |
0.217102 | + | 0.976149i | \(0.430340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6999 | + | 10.6801i | 0.743407 | + | 0.540117i | ||||
\(392\) | 1.09144 | + | 3.35909i | 0.0551258 | + | 0.169660i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.242825 | + | 0.747337i | 0.0122333 | + | 0.0376503i | ||||
\(395\) | 0.247944 | − | 7.25695i | 0.0124754 | − | 0.365137i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.05796 | + | 18.6445i | −0.304040 | + | 0.935740i | 0.675993 | + | 0.736908i | \(0.263715\pi\) |
−0.980034 | + | 0.198832i | \(0.936285\pi\) | |||||||
\(398\) | −0.683615 | + | 0.496675i | −0.0342665 | + | 0.0248961i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.3545 | − | 1.32409i | −0.967725 | − | 0.0662046i | ||||
\(401\) | 14.4239 | 0.720297 | 0.360148 | − | 0.932895i | \(-0.382726\pi\) | ||||
0.360148 | + | 0.932895i | \(0.382726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.77375 | − | 5.45903i | 0.0883566 | − | 0.271934i | ||||
\(404\) | −0.437224 | + | 1.34564i | −0.0217527 | + | 0.0669479i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.140328 | + | 0.431885i | 0.00696436 | + | 0.0214341i | ||||
\(407\) | −27.4179 | −1.35906 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.5507 | + | 16.3841i | 1.11506 | + | 0.810140i | 0.983453 | − | 0.181162i | \(-0.0579858\pi\) |
0.131609 | + | 0.991302i | \(0.457986\pi\) | |||||||
\(410\) | −0.770865 | + | 0.221671i | −0.0380703 | + | 0.0109475i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.25062 | + | 0.908630i | 0.0616137 | + | 0.0447650i | ||||
\(413\) | −9.11481 | − | 6.62229i | −0.448510 | − | 0.325862i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.25410 | − | 13.6975i | −0.454266 | − | 0.672383i | ||||
\(416\) | −6.21773 | − | 4.51745i | −0.304850 | − | 0.221486i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.32069 | 0.162420 | ||||||||
\(419\) | 11.2137 | + | 34.5121i | 0.547823 | + | 1.68603i | 0.714182 | + | 0.699960i | \(0.246799\pi\) |
−0.166359 | + | 0.986065i | \(0.553201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.04324 | + | 3.21077i | −0.0508445 | + | 0.156483i | −0.973255 | − | 0.229728i | \(-0.926216\pi\) |
0.922410 | + | 0.386211i | \(0.126216\pi\) | |||||||
\(422\) | −0.600649 | + | 1.84861i | −0.0292391 | + | 0.0899888i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.32422 | −0.0643099 | ||||||||
\(425\) | 20.3527 | + | 17.0258i | 0.987253 | + | 0.825872i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.18527 | − | 5.22040i | 0.347719 | − | 0.252633i | ||||
\(428\) | 7.31755 | − | 22.5211i | 0.353707 | − | 1.08860i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.658606 | + | 0.844288i | −0.0317608 | + | 0.0407152i | ||||
\(431\) | 7.93015 | + | 24.4065i | 0.381982 | + | 1.17562i | 0.938646 | + | 0.344881i | \(0.112081\pi\) |
−0.556665 | + | 0.830737i | \(0.687919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.3010 | − | 37.8587i | −0.591150 | − | 1.81937i | −0.573027 | − | 0.819536i | \(-0.694231\pi\) |
−0.0181229 | − | 0.999836i | \(-0.505769\pi\) | |||||||
\(434\) | 0.123270 | + | 0.0895606i | 0.00591713 | + | 0.00429905i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.89850 | − | 2.83243i | 0.186704 | − | 0.135649i | ||||
\(437\) | 17.6407 | + | 12.8167i | 0.843867 | + | 0.613106i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.4402 | + | 19.9365i | −1.30965 | + | 0.951516i | −0.309649 | + | 0.950851i | \(0.600212\pi\) |
−1.00000 | 0.000665125i | \(0.999788\pi\) | ||||||||
\(440\) | −4.36156 | − | 1.58376i | −0.207929 | − | 0.0755026i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.06454 | + | 3.27633i | 0.0506352 | + | 0.155839i | ||||
\(443\) | 28.9300 | 1.37451 | 0.687253 | − | 0.726418i | \(-0.258816\pi\) | ||||
0.687253 | + | 0.726418i | \(0.258816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.3142 | − | 27.3234i | 1.01039 | − | 1.29525i | ||||
\(446\) | 0.141936 | − | 0.436835i | 0.00672088 | − | 0.0206847i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.22332 | + | 3.79497i | −0.246779 | + | 0.179295i | ||||
\(449\) | 10.2089 | 0.481788 | 0.240894 | − | 0.970551i | \(-0.422559\pi\) | ||||
0.240894 | + | 0.970551i | \(0.422559\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.31639 | 0.438692 | ||||||||
\(452\) | 25.6853 | − | 18.6615i | 1.20814 | − | 0.877762i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.577074 | + | 1.77605i | −0.0270834 | + | 0.0833542i | ||||
\(455\) | −8.26470 | − | 3.00105i | −0.387455 | − | 0.140692i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.4952 | 1.52006 | 0.760030 | − | 0.649888i | \(-0.225184\pi\) | ||||
0.760030 | + | 0.649888i | \(0.225184\pi\) | |||||||
\(458\) | 0.255618 | + | 0.786712i | 0.0119442 | + | 0.0367606i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.48568 | − | 12.5601i | −0.395647 | − | 0.585618i | ||||
\(461\) | −0.566772 | + | 0.411784i | −0.0263972 | + | 0.0191787i | −0.600906 | − | 0.799320i | \(-0.705193\pi\) |
0.574508 | + | 0.818499i | \(0.305193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.75659 | − | 1.27623i | −0.0816355 | − | 0.0593117i | 0.546219 | − | 0.837642i | \(-0.316067\pi\) |
−0.627854 | + | 0.778331i | \(0.716067\pi\) | |||||||
\(464\) | 11.7210 | − | 8.51578i | 0.544132 | − | 0.395335i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.07001 | + | 0.777408i | 0.0495673 | + | 0.0360127i | ||||
\(467\) | 1.19809 | + | 3.68734i | 0.0554410 | + | 0.170630i | 0.974943 | − | 0.222456i | \(-0.0714075\pi\) |
−0.919502 | + | 0.393086i | \(0.871407\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.887597 | − | 2.73174i | −0.0409854 | − | 0.126140i | ||||
\(470\) | −1.50749 | − | 2.23132i | −0.0695356 | − | 0.102923i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.28739 | − | 7.03986i | 0.105286 | − | 0.324036i | ||||
\(473\) | 10.0618 | − | 7.31036i | 0.462644 | − | 0.336131i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.4244 | + | 20.4318i | 1.12067 | + | 0.937476i | ||||
\(476\) | 9.01870 | 0.413371 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.750911 | + | 2.31107i | −0.0343459 | + | 0.105706i | ||||
\(479\) | 6.79817 | − | 20.9226i | 0.310617 | − | 0.955979i | −0.666905 | − | 0.745143i | \(-0.732381\pi\) |
0.977521 | − | 0.210836i | \(-0.0676187\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5480 | − | 32.4634i | −0.480948 | − | 1.48020i | ||||
\(482\) | 1.02310 | 0.0466010 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.07156 | + | 2.95816i | 0.185071 | + | 0.134462i | ||||
\(485\) | 0.766483 | − | 22.4338i | 0.0348042 | − | 1.01867i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.9759 | − | 16.6929i | −1.04114 | − | 0.756430i | −0.0706291 | − | 0.997503i | \(-0.522501\pi\) |
−0.970507 | + | 0.241073i | \(0.922501\pi\) | |||||||
\(488\) | 4.72075 | + | 3.42982i | 0.213698 | + | 0.155261i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.22053 | + | 1.56464i | −0.0551380 | + | 0.0706831i | ||||
\(491\) | −11.3641 | − | 8.25653i | −0.512856 | − | 0.372612i | 0.301050 | − | 0.953608i | \(-0.402663\pi\) |
−0.813906 | + | 0.580997i | \(0.802663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.8167 | −0.892498 | ||||||||
\(494\) | 1.27751 | + | 3.93176i | 0.0574778 | + | 0.176898i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50219 | − | 4.62326i | 0.0674503 | − | 0.207591i | ||||
\(497\) | −1.14657 | + | 3.52878i | −0.0514307 | + | 0.158287i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0842 | 0.585731 | 0.292866 | − | 0.956154i | \(-0.405391\pi\) | ||||
0.292866 | + | 0.956154i | \(0.405391\pi\) | |||||||
\(500\) | −11.1114 | − | 19.1455i | −0.496918 | − | 0.856211i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.659929 | + | 0.479467i | −0.0294541 | + | 0.0213996i | ||||
\(503\) | −3.80226 | + | 11.7022i | −0.169534 | + | 0.521773i | −0.999342 | − | 0.0362767i | \(-0.988450\pi\) |
0.829807 | + | 0.558050i | \(0.188450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.53570 | + | 0.441607i | −0.0683376 | + | 0.0196512i | ||||
\(506\) | −0.551653 | − | 1.69781i | −0.0245240 | − | 0.0754770i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.34850 | + | 7.22793i | 0.104198 | + | 0.320688i | ||||
\(509\) | 0.0634186 | + | 0.0460763i | 0.00281098 | + | 0.00204230i | 0.589190 | − | 0.807995i | \(-0.299447\pi\) |
−0.586379 | + | 0.810037i | \(0.699447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.30509 | + | 4.58092i | −0.278921 | + | 0.202648i | ||||
\(512\) | −8.80600 | − | 6.39793i | −0.389174 | − | 0.282751i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.09043 | − | 2.24533i | 0.136313 | − | 0.0990372i | ||||
\(515\) | −0.0596143 | + | 1.74482i | −0.00262692 | + | 0.0768861i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.66515 | + | 29.7463i | 0.425073 | + | 1.30824i | ||||
\(518\) | 0.906103 | 0.0398119 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.197259 | − | 5.77347i | 0.00865036 | − | 0.253183i | ||||
\(521\) | −5.59919 | + | 17.2325i | −0.245305 | + | 0.754971i | 0.750281 | + | 0.661119i | \(0.229918\pi\) |
−0.995586 | + | 0.0938524i | \(0.970082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.40913 | + | 6.83613i | −0.411432 | + | 0.298923i | −0.774181 | − | 0.632964i | \(-0.781838\pi\) |
0.362749 | + | 0.931887i | \(0.381838\pi\) | |||||||
\(524\) | −24.6490 | −1.07680 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.92834 | −0.127682 | ||||||||
\(527\) | −5.37929 | + | 3.90828i | −0.234326 | + | 0.170247i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.48500 | + | 10.7257i | −0.151522 | + | 0.466336i | ||||
\(530\) | −0.416502 | − | 0.616487i | −0.0180917 | − | 0.0267785i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.8229 | 0.469232 | ||||||||
\(533\) | 3.58413 | + | 11.0308i | 0.155246 | + | 0.477797i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.7020 | − | 7.39090i | 1.11120 | − | 0.319536i | ||||
\(536\) | 1.52672 | − | 1.10923i | 0.0659442 | − | 0.0479113i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.57541 | − | 1.14460i | −0.0679208 | − | 0.0493473i | ||||
\(539\) | 18.6466 | − | 13.5476i | 0.803167 | − | 0.583535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6812 | − | 17.2054i | −1.01814 | − | 0.739719i | −0.0522359 | − | 0.998635i | \(-0.516635\pi\) |
−0.965900 | + | 0.258916i | \(0.916635\pi\) | |||||||
\(542\) | 0.146412 | + | 0.450608i | 0.00628891 | + | 0.0193553i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.75115 | + | 8.46718i | 0.117955 | + | 0.363027i | ||||
\(545\) | 5.11542 | + | 1.85750i | 0.219121 | + | 0.0795665i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.72908 | − | 11.4769i | 0.159444 | − | 0.490717i | −0.839140 | − | 0.543915i | \(-0.816941\pi\) |
0.998584 | + | 0.0531977i | \(0.0169413\pi\) | |||||||
\(548\) | 18.9955 | − | 13.8010i | 0.811448 | − | 0.589551i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.634510 | − | 2.52864i | −0.0270556 | − | 0.107822i | ||||
\(551\) | −23.7810 | −1.01311 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.861290 | − | 2.65078i | 0.0366258 | − | 0.112723i | ||||
\(554\) | 0.390096 | − | 1.20059i | 0.0165736 | − | 0.0510083i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.85168 | + | 8.77655i | 0.120938 | + | 0.372209i | ||||
\(557\) | 41.4154 | 1.75483 | 0.877413 | − | 0.479737i | \(-0.159268\pi\) | ||||
0.877413 | + | 0.479737i | \(0.159268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5265 | + | 9.10106i | 0.529816 | + | 0.384934i | ||||
\(560\) | −6.99939 | − | 2.54160i | −0.295778 | − | 0.107402i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.57816 | − | 1.87314i | −0.108753 | − | 0.0790137i | ||||
\(563\) | −26.0072 | − | 18.8954i | −1.09607 | − | 0.796345i | −0.115660 | − | 0.993289i | \(-0.536898\pi\) |
−0.980415 | + | 0.196944i | \(0.936898\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.7030 | + | 12.2381i | 1.41790 | + | 0.514862i | ||||
\(566\) | −0.149813 | − | 0.108846i | −0.00629712 | − | 0.00457513i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.43773 | −0.102285 | ||||||||
\(569\) | −6.52273 | − | 20.0749i | −0.273447 | − | 0.841583i | −0.989626 | − | 0.143667i | \(-0.954111\pi\) |
0.716179 | − | 0.697916i | \(-0.245889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.64795 | + | 23.5380i | −0.320057 | + | 0.985034i | 0.653566 | + | 0.756870i | \(0.273272\pi\) |
−0.973623 | + | 0.228164i | \(0.926728\pi\) | |||||||
\(572\) | −10.3149 | + | 31.7459i | −0.431286 | + | 1.32736i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.307886 | −0.0128509 | ||||||||
\(575\) | 6.38894 | − | 15.8820i | 0.266437 | − | 0.662327i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.1861 | − | 11.0333i | 0.632205 | − | 0.459324i | −0.224959 | − | 0.974368i | \(-0.572225\pi\) |
0.857163 | + | 0.515045i | \(0.172225\pi\) | |||||||
\(578\) | 0.488830 | − | 1.50446i | 0.0203327 | − | 0.0625775i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.5388 | + | 5.64242i | 0.645215 | + | 0.234289i | ||||
\(581\) | −1.96078 | − | 6.03467i | −0.0813470 | − | 0.250360i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.67036 | + | 8.21853i | 0.110595 | + | 0.340377i | ||||
\(584\) | −4.14247 | − | 3.00968i | −0.171417 | − | 0.124541i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.225886 | − | 0.164116i | 0.00933127 | − | 0.00677956i | ||||
\(587\) | 11.9388 | + | 8.67406i | 0.492768 | + | 0.358017i | 0.806248 | − | 0.591578i | \(-0.201495\pi\) |
−0.313480 | + | 0.949595i | \(0.601495\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.45543 | + | 4.69014i | −0.265991 | + | 0.193254i | ||||
\(590\) | 3.99683 | − | 1.14933i | 0.164547 | − | 0.0473173i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.93313 | − | 27.4933i | −0.367149 | − | 1.12997i | ||||
\(593\) | −8.01859 | −0.329284 | −0.164642 | − | 0.986353i | \(-0.552647\pi\) | ||||
−0.164642 | + | 0.986353i | \(0.552647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.70199 | + | 8.43983i | 0.233759 | + | 0.345999i | ||||
\(596\) | −7.06544 | + | 21.7452i | −0.289412 | + | 0.890718i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.79802 | − | 1.30634i | 0.0735265 | − | 0.0534201i | ||||
\(599\) | 1.28951 | 0.0526878 | 0.0263439 | − | 0.999653i | \(-0.491614\pi\) | ||||
0.0263439 | + | 0.999653i | \(0.491614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.8813 | −0.688603 | −0.344302 | − | 0.938859i | \(-0.611884\pi\) | ||||
−0.344302 | + | 0.938859i | \(0.611884\pi\) | |||||||
\(602\) | −0.332522 | + | 0.241591i | −0.0135526 | + | 0.00984652i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.9711 | + | 46.0764i | −0.609167 | + | 1.87482i | ||||
\(605\) | −0.194082 | + | 5.68050i | −0.00789055 | + | 0.230945i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.499318 | −0.0202667 | −0.0101334 | − | 0.999949i | \(-0.503226\pi\) | ||||
−0.0101334 | + | 0.999949i | \(0.503226\pi\) | |||||||
\(608\) | 3.30153 | + | 10.1611i | 0.133895 | + | 0.412085i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.111946 | + | 3.27650i | −0.00453257 | + | 0.132662i | ||||
\(611\) | −31.5019 | + | 22.8875i | −1.27443 | + | 0.925929i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.1866 | − | 16.1195i | −0.896108 | − | 0.651061i | 0.0413552 | − | 0.999145i | \(-0.486832\pi\) |
−0.937463 | + | 0.348084i | \(0.886832\pi\) | |||||||
\(614\) | 1.74860 | − | 1.27043i | 0.0705679 | − | 0.0512706i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.44097 | − | 1.04692i | −0.0580582 | − | 0.0421818i | ||||
\(617\) | 8.75151 | + | 26.9344i | 0.352323 | + | 1.08434i | 0.957546 | + | 0.288282i | \(0.0930840\pi\) |
−0.605223 | + | 0.796056i | \(0.706916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.114894 | − | 0.353606i | −0.00461796 | − | 0.0142126i | 0.948721 | − | 0.316115i | \(-0.102378\pi\) |
−0.953339 | + | 0.301902i | \(0.902378\pi\) | |||||||
\(620\) | 5.33087 | − | 1.53295i | 0.214093 | − | 0.0615647i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.776966 | + | 2.39125i | −0.0311535 | + | 0.0958806i | ||||
\(623\) | 10.7613 | − | 7.81853i | 0.431142 | − | 0.313243i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.8915 | − | 22.5028i | 0.435660 | − | 0.900111i | ||||
\(626\) | −3.88043 | −0.155093 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.6842 | − | 42.1157i | 0.546059 | − | 1.68060i | ||||
\(629\) | −12.2188 | + | 37.6056i | −0.487195 | + | 1.49943i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.08354 | + | 15.6455i | 0.202373 | + | 0.622839i | 0.999811 | + | 0.0194386i | \(0.00618787\pi\) |
−0.797438 | + | 0.603400i | \(0.793812\pi\) | |||||||
\(632\) | 1.83120 | 0.0728411 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.991042 | + | 0.720034i | 0.0393593 | + | 0.0285962i | ||||
\(635\) | −5.27919 | + | 6.76755i | −0.209498 | + | 0.268562i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.2142 | + | 16.8661i | 0.919780 | + | 0.668259i | ||||
\(638\) | 1.57512 | + | 1.14439i | 0.0623598 | + | 0.0453070i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.337558 | − | 9.87982i | 0.0133431 | − | 0.390534i | ||||
\(641\) | −1.63910 | − | 1.19088i | −0.0647407 | − | 0.0470368i | 0.554944 | − | 0.831888i | \(-0.312740\pi\) |
−0.619685 | + | 0.784851i | \(0.712740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.2034 | −1.30941 | −0.654706 | − | 0.755883i | \(-0.727208\pi\) | ||||
−0.654706 | + | 0.755883i | \(0.727208\pi\) | |||||||
\(644\) | −1.79797 | − | 5.53357i | −0.0708498 | − | 0.218053i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.47986 | − | 4.55455i | 0.0582244 | − | 0.179196i | ||||
\(647\) | 12.5398 | − | 38.5936i | 0.492992 | − | 1.51727i | −0.327072 | − | 0.944999i | \(-0.606062\pi\) |
0.820064 | − | 0.572273i | \(-0.193938\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.3042 | −1.89611 | ||||||||
\(650\) | 2.74986 | − | 1.72407i | 0.107859 | − | 0.0676237i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.30298 | + | 0.946669i | −0.0510286 | + | 0.0370744i | ||||
\(653\) | 2.87297 | − | 8.84208i | 0.112428 | − | 0.346017i | −0.878974 | − | 0.476870i | \(-0.841771\pi\) |
0.991402 | + | 0.130852i | \(0.0417714\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.5841 | − | 23.0669i | −0.608921 | − | 0.901297i | ||||
\(656\) | 3.03540 | + | 9.34201i | 0.118513 | + | 0.364744i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.319412 | − | 0.983049i | −0.0124520 | − | 0.0383232i | ||||
\(659\) | −2.81185 | − | 2.04293i | −0.109534 | − | 0.0795811i | 0.531670 | − | 0.846952i | \(-0.321565\pi\) |
−0.641204 | + | 0.767371i | \(0.721565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.29515 | + | 2.39407i | −0.128166 | + | 0.0931184i | −0.650022 | − | 0.759916i | \(-0.725240\pi\) |
0.521855 | + | 0.853034i | \(0.325240\pi\) | |||||||
\(662\) | −0.568859 | − | 0.413300i | −0.0221093 | − | 0.0160634i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.37266 | − | 2.45038i | 0.130885 | − | 0.0950932i | ||||
\(665\) | 6.84269 | + | 10.1282i | 0.265348 | + | 0.392756i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.95065 | + | 12.1589i | 0.152970 | + | 0.470793i | ||||
\(668\) | −49.8267 | −1.92785 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.996590 | + | 0.361879i | 0.0385016 | + | 0.0139806i | ||||
\(671\) | 11.7669 | − | 36.2148i | 0.454257 | − | 1.39806i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.3003 | + | 12.5694i | −0.666877 | + | 0.484514i | −0.868978 | − | 0.494850i | \(-0.835223\pi\) |
0.202102 | + | 0.979365i | \(0.435223\pi\) | |||||||
\(674\) | −1.03508 | −0.0398699 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.8170 | −0.608346 | ||||||||
\(677\) | −16.4438 | + | 11.9472i | −0.631988 | + | 0.459166i | −0.857088 | − | 0.515169i | \(-0.827729\pi\) |
0.225100 | + | 0.974336i | \(0.427729\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.66256 | − | 8.19451i | 0.102180 | − | 0.314476i | ||||
\(680\) | −4.11596 | + | 5.27638i | −0.157840 | + | 0.202340i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.653271 | 0.0250150 | ||||||||
\(683\) | 5.85868 | + | 18.0312i | 0.224176 | + | 0.689943i | 0.998374 | + | 0.0569998i | \(0.0181535\pi\) |
−0.774198 | + | 0.632943i | \(0.781847\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.9250 | + | 9.05068i | 0.952334 | + | 0.345809i | ||||
\(686\) | −1.30494 | + | 0.948096i | −0.0498229 | + | 0.0361985i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.6087 | + | 7.70770i | 0.404455 | + | 0.293853i | ||||
\(689\) | −8.70359 | + | 6.32353i | −0.331580 | + | 0.240907i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.9893 | − | 8.71071i | −0.456093 | − | 0.331371i | 0.335904 | − | 0.941896i | \(-0.390958\pi\) |
−0.791997 | + | 0.610525i | \(0.790958\pi\) | |||||||
\(692\) | 0.251429 | + | 0.773818i | 0.00955789 | + | 0.0294162i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.697811 | − | 2.14764i | −0.0264885 | − | 0.0815234i | ||||
\(695\) | −6.41028 | + | 8.21754i | −0.243156 | + | 0.311709i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.15185 | − | 12.7781i | 0.157262 | − | 0.484004i | ||||
\(698\) | −1.90106 | + | 1.38120i | −0.0719560 | + | 0.0522791i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.06802 | − | 8.24145i | −0.0781638 | − | 0.311497i | ||||
\(701\) | −31.3996 | −1.18595 | −0.592973 | − | 0.805222i | \(-0.702046\pi\) | ||||
−0.592973 | + | 0.805222i | \(0.702046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.6632 | + | 45.1287i | −0.553033 | + | 1.70206i | ||||
\(704\) | −8.55395 | + | 26.3264i | −0.322389 | + | 0.992212i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.567846 | − | 1.74765i | −0.0213712 | − | 0.0657737i | ||||
\(707\) | −0.613363 | −0.0230679 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.4944 | − | 14.8900i | −0.769682 | − | 0.559207i | 0.132183 | − | 0.991225i | \(-0.457801\pi\) |
−0.901865 | + | 0.432019i | \(0.857801\pi\) | |||||||
\(710\) | −0.766731 | − | 1.13488i | −0.0287749 | − | 0.0425913i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.07021 | + | 5.13681i | 0.264967 | + | 0.192510i | ||||
\(713\) | 3.47041 | + | 2.52140i | 0.129968 | + | 0.0944272i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.2297 | + | 10.4183i | −1.35491 | + | 0.389620i | ||||
\(716\) | 23.7869 | + | 17.2822i | 0.888959 | + | 0.645867i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.91168 | 0.0713432 | ||||||||
\(719\) | 1.27535 | + | 3.92511i | 0.0475624 | + | 0.146382i | 0.972017 | − | 0.234910i | \(-0.0754794\pi\) |
−0.924455 | + | 0.381292i | \(0.875479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.207084 | + | 0.637339i | −0.00771221 | + | 0.0237358i | ||||
\(722\) | 0.944008 | − | 2.90536i | 0.0351323 | − | 0.108126i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.46361 | −0.0543945 | ||||||||
\(725\) | 4.54404 | + | 18.1088i | 0.168761 | + | 0.672545i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.6106 | + | 13.5214i | −0.690227 | + | 0.501479i | −0.876735 | − | 0.480974i | \(-0.840283\pi\) |
0.186508 | + | 0.982454i | \(0.440283\pi\) | |||||||
\(728\) | 0.685223 | − | 2.10890i | 0.0253961 | − | 0.0781610i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0982330 | − | 2.87514i | 0.00363577 | − | 0.106414i | ||||
\(731\) | −5.54260 | − | 17.0584i | −0.205000 | − | 0.630927i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.89145 | − | 8.89896i | −0.106798 | − | 0.328690i | 0.883350 | − | 0.468714i | \(-0.155282\pi\) |
−0.990148 | + | 0.140023i | \(0.955282\pi\) | |||||||
\(734\) | −0.524386 | − | 0.380989i | −0.0193554 | − | 0.0140625i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.64671 | − | 3.37604i | 0.171280 | − | 0.124442i | ||||
\(737\) | −9.96291 | − | 7.23847i | −0.366988 | − | 0.266633i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.1657 | − | 27.7290i | 1.40395 | − | 1.02003i | 0.409781 | − | 0.912184i | \(-0.365605\pi\) |
0.994168 | − | 0.107844i | \(-0.0343948\pi\) | |||||||
\(740\) | 20.2886 | − | 26.0086i | 0.745823 | − | 0.956094i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.0882496 | − | 0.271604i | −0.00323974 | − | 0.00997091i | ||||
\(743\) | −2.39450 | −0.0878455 | −0.0439228 | − | 0.999035i | \(-0.513986\pi\) | ||||
−0.0439228 | + | 0.999035i | \(0.513986\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.8165 | + | 7.13627i | −0.909208 | + | 0.261453i | ||||
\(746\) | −0.908366 | + | 2.79566i | −0.0332576 | + | 0.102356i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 31.2821 | − | 22.7278i | 1.14379 | − | 0.831011i | ||||
\(749\) | 10.2655 | 0.375092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.21632 | −0.263327 | −0.131664 | − | 0.991294i | \(-0.542032\pi\) | ||||
−0.131664 | + | 0.991294i | \(0.542032\pi\) | |||||||
\(752\) | −26.6790 | + | 19.3835i | −0.972885 | + | 0.706842i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.749019 | + | 2.30524i | −0.0272777 | + | 0.0839520i | ||||
\(755\) | −52.5843 | + | 15.1212i | −1.91374 | + | 0.550317i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3742 | 0.486094 | 0.243047 | − | 0.970015i | \(-0.421853\pi\) | ||||
0.243047 | + | 0.970015i | \(0.421853\pi\) | |||||||
\(758\) | −0.253145 | − | 0.779101i | −0.00919465 | − | 0.0282982i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.93936 | + | 6.33193i | −0.179170 | + | 0.229683i | ||||
\(761\) | 17.5994 | − | 12.7867i | 0.637978 | − | 0.463518i | −0.221177 | − | 0.975234i | \(-0.570990\pi\) |
0.859155 | + | 0.511716i | \(0.170990\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69003 | + | 1.22788i | 0.0611831 | + | 0.0444521i | ||||
\(764\) | 4.36499 | − | 3.17135i | 0.157920 | − | 0.114735i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.95886 | + | 2.14973i | 0.106908 | + | 0.0776730i | ||||
\(767\) | −18.5832 | − | 57.1932i | −0.671000 | − | 2.06513i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.38814 | + | 13.5053i | 0.158240 | + | 0.487014i | 0.998475 | − | 0.0552094i | \(-0.0175826\pi\) |
−0.840234 | + | 0.542223i | \(0.817583\pi\) | |||||||
\(770\) | 0.0341706 | − | 1.00012i | 0.00123142 | − | 0.0360419i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.69046 | + | 26.7465i | −0.312777 | + | 0.962627i | ||||
\(773\) | 18.4752 | − | 13.4230i | 0.664505 | − | 0.482791i | −0.203676 | − | 0.979038i | \(-0.565289\pi\) |
0.868181 | + | 0.496247i | \(0.165289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.80495 | + | 4.01951i | 0.172599 | + | 0.144385i | ||||
\(776\) | 5.66089 | 0.203214 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.687616 | − | 2.11627i | 0.0246522 | − | 0.0758718i | ||||
\(779\) | 4.98243 | − | 15.3343i | 0.178514 | − | 0.549410i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.91582 | + | 15.1293i | 0.175902 | + | 0.541370i | ||||
\(782\) | −2.57451 | −0.0920644 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.6602 | + | 14.2839i | 0.702148 | + | 0.510141i | ||||
\(785\) | 48.0642 | − | 13.8214i | 1.71548 | − | 0.493306i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.1279 | + | 22.6157i | 1.10959 | + | 0.806163i | 0.982599 | − | 0.185741i | \(-0.0594685\pi\) |
0.126990 | + | 0.991904i | \(0.459469\pi\) | |||||||
\(788\) | 8.88339 | + | 6.45416i | 0.316458 | + | 0.229920i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.575959 | + | 0.852508i | 0.0204917 | + | 0.0303309i | ||||
\(791\) | 11.1348 | + | 8.08988i | 0.395906 | + | 0.287643i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.4060 | 1.68344 | ||||||||
\(794\) | −0.858349 | − | 2.64173i | −0.0304617 | − | 0.0937514i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.64878 | + | 11.2298i | −0.129327 | + | 0.398029i | ||||
\(797\) | 0.577055 | − | 1.77599i | 0.0204404 | − | 0.0629089i | −0.940316 | − | 0.340302i | \(-0.889471\pi\) |
0.960756 | + | 0.277393i | \(0.0894706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.1063 | 1.59575 | ||||||||
\(800\) | 7.10661 | − | 4.45561i | 0.251257 | − | 0.157530i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.65340 | + | 1.20127i | −0.0583837 | + | 0.0424182i | ||||
\(803\) | −10.3255 | + | 31.7786i | −0.364379 | + | 1.12144i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.04165 | − | 5.18112i | 0.142449 | − | 0.182610i | ||||
\(806\) | 0.251321 | + | 0.773487i | 0.00885241 | + | 0.0272449i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.124528 | − | 0.383258i | −0.00438089 | − | 0.0134830i | ||||
\(809\) | 28.4381 | + | 20.6615i | 0.999831 | + | 0.726420i | 0.962052 | − | 0.272866i | \(-0.0879717\pi\) |
0.0377789 | + | 0.999286i | \(0.487972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.33270 | − | 3.87443i | 0.187256 | − | 0.136050i | −0.490208 | − | 0.871606i | \(-0.663079\pi\) |
0.677464 | + | 0.735556i | \(0.263079\pi\) | |||||||
\(812\) | 5.13370 | + | 3.72985i | 0.180158 | + | 0.130892i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.14290 | − | 2.28345i | 0.110158 | − | 0.0800348i | ||||
\(815\) | −1.70970 | − | 0.620822i | −0.0598883 | − | 0.0217465i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.65141 | − | 20.4709i | −0.232703 | − | 0.716187i | ||||
\(818\) | −3.94949 | −0.138091 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.89389 | + | 8.83750i | −0.240745 | + | 0.308619i | ||||
\(821\) | −1.62463 | + | 5.00011i | −0.0567001 | + | 0.174505i | −0.975396 | − | 0.220461i | \(-0.929244\pi\) |
0.918696 | + | 0.394966i | \(0.129244\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.9536 | − | 13.0440i | 0.625823 | − | 0.454687i | −0.229128 | − | 0.973396i | \(-0.573587\pi\) |
0.854951 | + | 0.518709i | \(0.173587\pi\) | |||||||
\(824\) | −0.440283 | −0.0153380 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.59635 | 0.0555440 | ||||||||
\(827\) | −5.30922 | + | 3.85738i | −0.184620 | + | 0.134134i | −0.676256 | − | 0.736666i | \(-0.736399\pi\) |
0.491637 | + | 0.870800i | \(0.336399\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.74316 | − | 23.8310i | 0.268931 | − | 0.827685i | −0.721831 | − | 0.692070i | \(-0.756699\pi\) |
0.990762 | − | 0.135615i | \(-0.0433010\pi\) | |||||||
\(830\) | 2.20156 | + | 0.799423i | 0.0764172 | + | 0.0277484i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −34.4618 | −1.19475 | ||||||||
\(833\) | −10.2716 | − | 31.6126i | −0.355889 | − | 1.09531i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.5025 | − | 46.6285i | −1.09019 | − | 1.61365i | ||||
\(836\) | 37.5402 | − | 27.2745i | 1.29835 | − | 0.943310i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.15968 | − | 3.02219i | −0.143694 | − | 0.104400i | ||||
\(839\) | −34.0989 | + | 24.7743i | −1.17722 | + | 0.855303i | −0.991856 | − | 0.127366i | \(-0.959348\pi\) |
−0.185368 | + | 0.982669i | \(0.559348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1813 | + | 8.85021i | 0.420044 | + | 0.305180i | ||||
\(842\) | −0.147816 | − | 0.454932i | −0.00509409 | − | 0.0156780i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.39327 | + | 25.8318i | 0.288908 | + | 0.889169i | ||||
\(845\) | −10.0002 | − | 14.8018i | −0.344016 | − | 0.509197i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.674189 | + | 2.07494i | −0.0231654 | + | 0.0712957i | ||||
\(848\) | −7.37109 | + | 5.35541i | −0.253124 | + | 0.183906i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.75098 | − | 0.256614i | −0.128657 | − | 0.00880180i | ||||
\(851\) | 25.5095 | 0.874454 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.3641 | − | 41.1306i | 0.457580 | − | 1.40829i | −0.410500 | − | 0.911861i | \(-0.634646\pi\) |
0.868080 | − | 0.496425i | \(-0.165354\pi\) | |||||||
\(854\) | −0.388871 | + | 1.19682i | −0.0133069 | + | 0.0409544i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.08415 | + | 6.41436i | 0.0712349 | + | 0.219238i | ||||
\(857\) | 39.2430 | 1.34052 | 0.670258 | − | 0.742128i | \(-0.266183\pi\) | ||||
0.670258 | + | 0.742128i | \(0.266183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.5617 | − | 30.9229i | −1.45219 | − | 1.05508i | −0.985314 | − | 0.170750i | \(-0.945381\pi\) |
−0.466872 | − | 0.884325i | \(-0.654619\pi\) | |||||||
\(860\) | −0.510928 | + | 14.9541i | −0.0174225 | + | 0.509931i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.94167 | − | 2.13725i | −0.100194 | − | 0.0727950i | ||||
\(863\) | −34.6861 | − | 25.2009i | −1.18073 | − | 0.857850i | −0.188476 | − | 0.982078i | \(-0.560355\pi\) |
−0.992254 | + | 0.124228i | \(0.960355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.565187 | + | 0.724530i | −0.0192169 | + | 0.0246348i | ||||
\(866\) | 4.56304 | + | 3.31524i | 0.155058 | + | 0.112657i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.12917 | 0.0722686 | ||||||||
\(869\) | −3.69270 | − | 11.3650i | −0.125266 | − | 0.385530i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.73766 | − | 14.5810i | 0.160530 | − | 0.494059i | ||||
\(872\) | −0.424118 | + | 1.30530i | −0.0143624 | + | 0.0442031i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.08955 | −0.104506 | ||||||||
\(875\) | 6.40498 | − | 7.14587i | 0.216528 | − | 0.241574i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.315771 | − | 0.229421i | 0.0106628 | − | 0.00774700i | −0.582441 | − | 0.812873i | \(-0.697902\pi\) |
0.593104 | + | 0.805126i | \(0.297902\pi\) | |||||||
\(878\) | 1.48508 | − | 4.57060i | 0.0501190 | − | 0.154250i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −30.6830 | + | 8.82324i | −1.03432 | + | 0.297431i | ||||
\(881\) | −13.8131 | − | 42.5124i | −0.465376 | − | 1.43228i | −0.858509 | − | 0.512798i | \(-0.828609\pi\) |
0.393133 | − | 0.919481i | \(-0.371391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.1224 | + | 31.1534i | 0.340645 | + | 1.04840i | 0.963874 | + | 0.266358i | \(0.0858202\pi\) |
−0.623230 | + | 0.782039i | \(0.714180\pi\) | |||||||
\(884\) | 38.9448 | + | 28.2951i | 1.30986 | + | 0.951666i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.31622 | + | 2.40938i | −0.111411 | + | 0.0809446i | ||||
\(887\) | −12.7121 | − | 9.23588i | −0.426830 | − | 0.310110i | 0.353550 | − | 0.935416i | \(-0.384974\pi\) |
−0.780380 | + | 0.625305i | \(0.784974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.66539 | + | 1.93652i | −0.0893944 | + | 0.0649488i | ||||
\(890\) | −0.167660 | + | 4.90717i | −0.00561999 | + | 0.164489i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.98337 | − | 6.10419i | −0.0664082 | − | 0.204383i | ||||
\(893\) | 54.1299 | 1.81139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.13387 | + | 33.1867i | −0.0379011 | + | 1.10931i | ||||
\(896\) | 1.17258 | − | 3.60884i | 0.0391733 | − | 0.120563i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.17024 | + | 0.850228i | −0.0390514 | + | 0.0283725i | ||||
\(899\) | −4.67839 | −0.156033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4623 | 0.415180 | ||||||||
\(902\) | −1.06793 | + | 0.775897i | −0.0355582 | + | 0.0258345i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.79430 | + | 8.59998i | −0.0929372 | + | 0.286031i | ||||
\(905\) | −0.925352 | − | 1.36966i | −0.0307597 | − | 0.0455291i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.50466 | −0.0499613 | −0.0249806 | − | 0.999688i | \(-0.507952\pi\) | ||||
−0.0249806 | + | 0.999688i | \(0.507952\pi\) | |||||||
\(908\) | 8.06385 | + | 24.8180i | 0.267608 | + | 0.823613i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.19731 | − | 0.344300i | 0.0396905 | − | 0.0114134i | ||||
\(911\) | 9.26400 | − | 6.73069i | 0.306930 | − | 0.222998i | −0.423648 | − | 0.905827i | \(-0.639251\pi\) |
0.730578 | + | 0.682829i | \(0.239251\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.0090 | − | 15.9904i | −0.728390 | − | 0.529207i | ||||
\(914\) | −3.72489 | + | 2.70629i | −0.123209 | + | 0.0895162i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.35142 | + | 6.79421i | 0.308980 | + | 0.224487i | ||||
\(917\) | −3.30200 | − | 10.1625i | −0.109042 | − | 0.335596i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.73660 | − | 20.7331i | −0.222220 | − | 0.683923i | −0.998562 | − | 0.0536108i | \(-0.982927\pi\) |
0.776342 | − | 0.630312i | \(-0.217073\pi\) | |||||||
\(920\) | 4.05797 | + | 1.47352i | 0.133787 | + | 0.0485805i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.0306740 | − | 0.0944049i | 0.00101019 | − | 0.00310906i | ||||
\(923\) | −16.0223 | + | 11.6409i | −0.527380 | + | 0.383164i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.1665 | + | 2.54266i | 1.22203 | + | 0.0836020i | ||||
\(926\) | 0.307645 | 0.0101098 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.93573 | + | 5.95756i | −0.0635434 | + | 0.195566i | ||||
\(929\) | 9.50249 | − | 29.2457i | 0.311767 | − | 0.959519i | −0.665298 | − | 0.746578i | \(-0.731696\pi\) |
0.977065 | − | 0.212941i | \(-0.0683043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.3264 | − | 37.9368i | −0.403982 | − | 1.24333i | ||||
\(932\) | 18.4817 | 0.605387 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.444429 | − | 0.322896i | −0.0145421 | − | 0.0105655i | ||||
\(935\) | 41.0469 | + | 14.9048i | 1.34238 | + | 0.487440i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.08284 | + | 2.23982i | 0.100712 | + | 0.0731716i | 0.637002 | − | 0.770862i | \(-0.280174\pi\) |
−0.536289 | + | 0.844034i | \(0.680174\pi\) | |||||||
\(938\) | 0.329252 | + | 0.239216i | 0.0107505 | + | 0.00781067i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −35.3692 | − | 12.8432i | −1.15362 | − | 0.418898i | ||||
\(941\) | −16.7501 | − | 12.1697i | −0.546037 | − | 0.396719i | 0.280285 | − | 0.959917i | \(-0.409571\pi\) |
−0.826322 | + | 0.563197i | \(0.809571\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.66792 | −0.282266 | ||||||||
\(944\) | −15.7381 | − | 48.4370i | −0.512233 | − | 1.57649i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.544553 | + | 1.67596i | −0.0177049 | + | 0.0544902i | ||||
\(947\) | −4.84640 | + | 14.9157i | −0.157487 | + | 0.484695i | −0.998404 | − | 0.0564684i | \(-0.982016\pi\) |
0.840917 | + | 0.541163i | \(0.182016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.5989 | −1.35036 | ||||||||
\(950\) | −4.50137 | − | 0.307950i | −0.146044 | − | 0.00999123i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.07809 | + | 1.50982i | −0.0673514 | + | 0.0489337i | ||||
\(953\) | 2.39552 | − | 7.37266i | 0.0775985 | − | 0.238824i | −0.904731 | − | 0.425983i | \(-0.859928\pi\) |
0.982330 | + | 0.187160i | \(0.0599282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.72752 | + | 2.07976i | 0.185338 | + | 0.0672994i | ||||
\(956\) | 10.4930 | + | 32.2941i | 0.339368 | + | 1.04447i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.963230 | + | 2.96452i | 0.0311205 | + | 0.0957792i | ||||
\(959\) | 8.23468 | + | 5.98285i | 0.265912 | + | 0.193196i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.8096 | − | 17.2987i | 0.768050 | − | 0.558021i | ||||
\(962\) | 3.91276 | + | 2.84279i | 0.126152 | + | 0.0916551i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.5661 | − | 8.40326i | 0.372519 | − | 0.270651i | ||||
\(965\) | −30.5242 | + | 8.77758i | −0.982609 | + | 0.282560i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9649 | − | 46.0571i | −0.481238 | − | 1.48110i | −0.837357 | − | 0.546657i | \(-0.815900\pi\) |
0.356119 | − | 0.934441i | \(-0.384100\pi\) | |||||||
\(968\) | −1.43340 | −0.0460712 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.78050 | + | 2.63541i | 0.0571683 | + | 0.0846179i | ||||
\(971\) | −7.82895 | + | 24.0950i | −0.251243 | + | 0.773246i | 0.743304 | + | 0.668954i | \(0.233258\pi\) |
−0.994547 | + | 0.104292i | \(0.966742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.23647 | + | 2.35143i | −0.103756 | + | 0.0753834i | ||||
\(974\) | 4.02394 | 0.128936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 40.1483 | 1.28511 | ||||||||
\(977\) | −0.945620 | + | 0.687033i | −0.0302531 | + | 0.0219801i | −0.602809 | − | 0.797885i | \(-0.705952\pi\) |
0.572556 | + | 0.819866i | \(0.305952\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.6232 | − | 54.2385i | 0.563239 | − | 1.73347i | ||||
\(980\) | −0.946853 | + | 27.7130i | −0.0302461 | + | 0.885259i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.99029 | 0.0635127 | ||||||||
\(983\) | 7.41464 | + | 22.8199i | 0.236490 | + | 0.727842i | 0.996920 | + | 0.0784223i | \(0.0249882\pi\) |
−0.760430 | + | 0.649420i | \(0.775012\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.423451 | + | 12.3938i | −0.0134923 | + | 0.394899i | ||||
\(986\) | 2.27157 | − | 1.65039i | 0.0723415 | − | 0.0525592i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 46.7358 | + | 33.9555i | 1.48686 | + | 1.08027i | ||||
\(989\) | −9.36148 | + | 6.80151i | −0.297678 | + | 0.216276i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6688 | + | 21.5556i | 0.942459 | + | 0.684737i | 0.949011 | − | 0.315242i | \(-0.102086\pi\) |
−0.00655196 | + | 0.999979i | \(0.502086\pi\) | |||||||
\(992\) | 0.649502 | + | 1.99896i | 0.0206217 | + | 0.0634671i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.162457 | − | 0.499991i | −0.00515282 | − | 0.0158588i | ||||
\(995\) | −12.8159 | + | 3.68535i | −0.406291 | + | 0.116834i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.6202 | + | 54.2295i | −0.558038 | + | 1.71747i | 0.129743 | + | 0.991548i | \(0.458585\pi\) |
−0.687782 | + | 0.725918i | \(0.741415\pi\) | |||||||
\(998\) | −1.49984 | + | 1.08970i | −0.0474765 | + | 0.0344937i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.2.h.d.136.2 | 12 | ||
3.2 | odd | 2 | 75.2.g.c.61.2 | yes | 12 | ||
15.2 | even | 4 | 375.2.i.d.199.4 | 24 | |||
15.8 | even | 4 | 375.2.i.d.199.3 | 24 | |||
15.14 | odd | 2 | 375.2.g.c.301.2 | 12 | |||
25.4 | even | 10 | 5625.2.a.q.1.3 | 6 | |||
25.16 | even | 5 | inner | 225.2.h.d.91.2 | 12 | ||
25.21 | even | 5 | 5625.2.a.p.1.4 | 6 | |||
75.29 | odd | 10 | 1875.2.a.k.1.4 | 6 | |||
75.38 | even | 20 | 375.2.i.d.49.4 | 24 | |||
75.41 | odd | 10 | 75.2.g.c.16.2 | ✓ | 12 | ||
75.47 | even | 20 | 1875.2.b.f.1249.6 | 12 | |||
75.53 | even | 20 | 1875.2.b.f.1249.7 | 12 | |||
75.59 | odd | 10 | 375.2.g.c.76.2 | 12 | |||
75.62 | even | 20 | 375.2.i.d.49.3 | 24 | |||
75.71 | odd | 10 | 1875.2.a.j.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.2 | ✓ | 12 | 75.41 | odd | 10 | ||
75.2.g.c.61.2 | yes | 12 | 3.2 | odd | 2 | ||
225.2.h.d.91.2 | 12 | 25.16 | even | 5 | inner | ||
225.2.h.d.136.2 | 12 | 1.1 | even | 1 | trivial | ||
375.2.g.c.76.2 | 12 | 75.59 | odd | 10 | |||
375.2.g.c.301.2 | 12 | 15.14 | odd | 2 | |||
375.2.i.d.49.3 | 24 | 75.62 | even | 20 | |||
375.2.i.d.49.4 | 24 | 75.38 | even | 20 | |||
375.2.i.d.199.3 | 24 | 15.8 | even | 4 | |||
375.2.i.d.199.4 | 24 | 15.2 | even | 4 | |||
1875.2.a.j.1.3 | 6 | 75.71 | odd | 10 | |||
1875.2.a.k.1.4 | 6 | 75.29 | odd | 10 | |||
1875.2.b.f.1249.6 | 12 | 75.47 | even | 20 | |||
1875.2.b.f.1249.7 | 12 | 75.53 | even | 20 | |||
5625.2.a.p.1.4 | 6 | 25.21 | even | 5 | |||
5625.2.a.q.1.3 | 6 | 25.4 | even | 10 |